On the necessity of estimating the transfer level in an allpass-FIR ADF bythe use of Lyapunov criteria

In this paper we present an analysis based on the indirect Lyapunov criteri a, that is used to study the convergence of an infinite impulse response (I IR) adaptive digital filter (ADF) based on estimation of the allpass system . The analysis is then extended to investigate the necessity of directly es timating the transfer level of the unknown system. We consider two cases of modeling the ADF. In the first system, the allpass section of the ADF esti mates only the real poles of the unknown system while in the second system, both real and complex poles the allpass section are estimated. From the an alysis and computer simulation, we realize that the poles of the ADF conver ge selectively to the poles of the unknown system, depending on the sign of the step size of adaptation. Using these results we proposed a new method to control the convergence of the poles the IIR ADF based on estimation of the allpass system.